Average Error: 0.1 → 0.1
Time: 32.2s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(3 \cdot z\right) \cdot z + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(3 \cdot z\right) \cdot z + x \cdot y
double f(double x, double y, double z) {
        double r19414027 = x;
        double r19414028 = y;
        double r19414029 = r19414027 * r19414028;
        double r19414030 = z;
        double r19414031 = r19414030 * r19414030;
        double r19414032 = r19414029 + r19414031;
        double r19414033 = r19414032 + r19414031;
        double r19414034 = r19414033 + r19414031;
        return r19414034;
}
↓
double f(double x, double y, double z) {
        double r19414035 = 3.0;
        double r19414036 = z;
        double r19414037 = r19414035 * r19414036;
        double r19414038 = r19414037 * r19414036;
        double r19414039 = x;
        double r19414040 = y;
        double r19414041 = r19414039 * r19414040;
        double r19414042 = r19414038 + r19414041;
        return r19414042;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(3.0 \cdot z\right) \cdot z + y \cdot x\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(3, z \cdot z, x \cdot y\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.1

    \[\leadsto \color{blue}{3 \cdot \left(z \cdot z\right) + x \cdot y}\]
  5. Using strategy rm

  6. Applied associate-*r*0.1

    \[\leadsto \color{blue}{\left(3 \cdot z\right) \cdot z} + x \cdot y\]

  7. Final simplification0.1

    \[\leadsto \left(3 \cdot z\right) \cdot z + x \cdot y\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"

  :herbie-target
  (+ (* (* 3.0 z) z) (* y x))

  (+ (+ (+ (* x y) (* z z)) (* z z)) (* z z)))